Exploring Complex Dynamical Systems via Nonconvex Optimization

TL;DR

This paper introduces an optimization-based machine learning approach to analyze complex dynamical systems, exemplified by a novel reaction-diffusion model that reveals new states and behaviors such as pattern formation and nonequilibrium states.

Contribution

It presents a new optimization-driven method for studying complex dynamical systems using machine learning tools, applied to a novel reaction-diffusion model.

Findings

Identified new states and behaviors in the reaction-diffusion model

Revealed pattern formation and dissipation-maximizing states

Discovered replication-like dynamical structures

Abstract

Cataloging the complex behaviors of dynamical systems can be challenging, even when they are well-described by a simple mechanistic model. If such a system is of limited analytical tractability, brute force simulation is often the only resort. We present an alternative, optimization-driven approach using tools from machine learning. We apply this approach to a novel, fully-optimizable, reaction-diffusion model which incorporates complex chemical reaction networks (termed "Dense Reaction-Diffusion Network" or "Dense RDN"). This allows us to systematically identify new states and behaviors, including pattern formation, dissipation-maximizing nonequilibrium states, and replication-like dynamical structures.